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Let L: R4 → R³ be the linear transformation defined by L((w, x, y, z)) = (w+x, y+z, w+y). a. Find a basis for ker L. What is dim(ker L)? b. Find a basis for im L. What is dim(im L)? c. Is L one-to-one? d. Is L onto?

Let L: R4 → R³ be the linear transformation defined by L((w, x, y, z)) = (w+x, y+z, w+y). a. Find a basis for ker L. What is dim(ker L)? b. Find a basis for im L. What is dim(im L)? c. Is L one-to-one? d. Is L onto?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please solve (c) and (d) part
Let L: R4 → R³ be the linear transformation defined by L((w,x, y, z)) = (w+x,y+z, w+y). a. Find a basis for ker L. What is dim(ker L)? b. Find a basis for im L. What is dim(im L)? c. Is L one-to-one? d. Is L onto?
Transcribed Image Text:Let L: R4 → R³ be the linear transformation defined by L((w,x, y, z)) = (w+x,y+z, w+y). a. Find a basis for ker L. What is dim(ker L)? b. Find a basis for im L. What is dim(im L)? c. Is L one-to-one? d. Is L onto?
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